ISTANBUL—With a U.S. attack on Syria on hold, Western-backed rebels said they feared they had lost their best chance of promptly ousting President Bashar al-Assad and sidelining Islamist extremists.

Rebels in Syria, already frustrated with delays in promised U.S. military aid, said on Wednesday that they gave up on the prospect of decisive foreign help after President Barack Obama asked Congress to delay a vote on striking Syria.

Mr. Obama put U.S. military momentum on pause on Tuesday night to give time for diplomacy to run its course, after a Russian proposal that Damascus hand over its chemical weapons, an effort to avert an attack.

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The Obama administration moved on Wednesday to follow up on the Russian proposal, with Secretary of State John Kerry heading to Geneva to meet Russian counterpart Sergei Lavrov.

Britain, France and the U.S. presented proposals for a Security Council resolution to Russia in New York on Wednesday, though a Western diplomat said negotiations on a text wouldn't begin until after the outcome of the Kerry-Lavrov meetings.

"The revolution is dead. It was sold," said Mohammad al-Daher, a commander in the rebels' Western-backed Free Syrian Army. "People used to assume that Assad will be gone, no question. But I wouldn't be surprised if the end result of these negotiations is that he remains as president and beyond that, turns into a national hero who saved his country."

The U.S. effort to arm rebels, authorized by Mr. Obama in June, appeared to have taken a step forward on Wednesday. The U.S. has started providing some arms to the Free Syrian Army, according to Khalid Saleh, spokesman for the Syrian Opposition Coalition. Mr. Saleh declined to provide details.

At a Seib & Wessel breakfast in Washington, D.C., Wednesday, Sen. John McCain (R., Ariz.) told reporters a post-Assad Syria is unlikely to fall into the hands of extremists and therefore the U.S. must do all it can to help the country's rebels.

U.S. officials said the program was delayed by initial objections from U.S. lawmakers and the difficulty of establishing secure pipelines to deliver arms to moderate fighters. The White House and the Central Intelligence Agency, which runs the arming program, declined to comment on reports that the first weapons had arrived.

The delay of a U.S. military strike gave congressional supporters a new opportunity to promote their cause. But the diplomatic maneuvering—and its offer of a possible way out for Mr. Assad—came as yet another disappointment for rebels in Syria.

Rebels based in the Damascus suburbs, counting on the U.S., had already adjusted their battle plans. Anticipating American airstrikes that in their view could help neutralize Mr. Assad's air force, the rebels plotted to follow with an assault on the Syrian capital that, they hoped, would crack the regime, according to these rebels.

Those expectations—as with other rebel hopes for game-changing U.S. intervention over the course of the 2½-year conflict—appear to have been unrealistic. Mr. Obama raised the idea of U.S. military action as a way to punish the Assad government for using chemical weapons—not to help the rebels in the battle on the ground.

U.S. military officials said the threat of a U.S. attack did affect the battle. The officials said they had seen some retreat in recent weeks by Mr. Assad's forces, moving from attacking positions to bunkers to shelter from a potential bombing campaign. As a result, the regime had been in less of a position to strike rebel positions, particularly around the city of Aleppo, the officials said.

But reports of new attacks this week by the Assad regime suggest the tide shifted as the threat of an immediate American attack receded.

Sen. John McCain (R., Ariz.), a leading advocate of military intervention, on Wednesday called the Russian plan a stalling tactic for the regime—and said that Syrian government forces resumed an air campaign against rebel positions on Tuesday and have stepped up ground attacks.

Mr. McCain said the military operations suggested that Mr. Assad believes he has a "free ride here" as the White House debates how to respond to a Russian proposal. Mr. McCain made the comments at an event hosted by The Wall Street Journal.

Sen. John McCain called Russia's plan for Syria to hand over its chemical weapons a stalling tactic at a Wall Street Journal event the morning after President Barack Obama addressed the nation over possible diplomatic progress. Jerry Seib reports on Lunch Break. Photo: AP.

The delay also benefits rebel extremists, Western-backed rebels said.

When the option of U.S. strikes emerged following the chemical-weapons attack on Aug. 21, al Qaeda-linked extremists and allied foreign jihadists in the opposition's largest foothold in northern Syria, fearing they could also be targets, went into hiding.

Free Syrian Army rebels said they believed the extremists re-emerged as emboldened and more-mobile guerrilla fighters.

The presence and strength of the extremists makes it harder for moderates to convince the West that Assad's defeat wouldn't turn Syria into a rogue nation dominated by terrorists. That concern also slows outside help, moderates say, as extremists sow Western doubts over the views and aims of the rebel movement.

"The jihadists benefit in all the chaos," said Samir Nachar, a Syrian Opposition Coalition member opposed to the rebel extremists. "They gain as the moderates waffle about waiting for the rest of the world."

The latest promise of intervention wasn't the first time the Syrian Opposition Coalition and its allied rebel forces adjusted their strategy in anticipation of U.S. aid. The Free Syrian Army regrouped and changed its leadership structure several times since the start of the civil war with the belief, rebel officials said, that by following a model encouraged by the West they could cleanse their ranks of extremists and guarantee a more consistent flow of funds and, eventually, arms.

Supreme Military Council leader Brig. Gen. Salim Idriss and other council members said support so far has been inadequate. U.S. officials said rebels had unfounded expectations and often misinterpreted their statements and actions.

Frustration over signs of a U.S. delay extended to the Arab world. "Please do not waste time in stalling or procrastination," Bahrain's Foreign Minister Sheik Khalid bin Ahmed al Khalifa said on behalf of the six-nation Gulf Cooperation Council, in a statement directed at Western nations involved in discussions over strikes on Syria.

Delegates of the broader 22-nation Arab League, meeting in Cairo, said they hoped Russia's proposal would succeed, but stressed that the international community still "must make a decision on binding and effective measures to ensure the cessation of hostilities in Syria immediately."

Syrian opposition leaders were skeptical the powerful Gulf states would make any game-changing moves on their own. "They don't move without U.S. consent. We've watched it, in plain sight, for three years now," said a senior member of the Syrian Opposition Coalition.

—Ellen Knickmeyer in Riyadh, Sam Dagher in Damascus, Julian E. Barnes and Adam Entous in Washington and Mohammad Alakraa in Beirut contributed to this article.

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